Abel-Jacobi theorem

Abstract

The Abel Jacobi theorem is an important result of algebraic geometry. The theory of divisors and the Riemann bilinear relations are fundamental to the developement of this result: if a point O is fixed in a Riemann compact surface X of genus g, the Abel Jaobi map identifies the Picard group: the quotient of divisors of a group of degree zero by the sub-group of divisors associated to meromorphic functions. The Riemann surface of genus g can be embedded in the Jacobian variety via the Abel-Jacobi. In fact, generally.the surface may be provided with an analytical structure.or algebraic varietie.